Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow
Turbomachine-Cascades (STCF)
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Standard configurations
Tenth standard configuration (Modified cambered
NACA 0006 cascade at subsonic and transonic flow conditions)
2D geomertry file: to be updated
Download data files:
stcf10_1x.zip (140 Kb) |
Time averaged blade surface pressure distributions
Aerodynamic lift coefficient and phase lead
Aerodynamic moment coefficient and phase lead
Time dependent blade surface MACH number |
File Information
The tenth Standard Configuration, included by proposal of Dr. J. M.
Verdon at the United Technologies Research Center [1987a,c], is a two-
dimensional compressor cascade of modified NACA 0006 profiles that operates
at subsonic inlet and exit conditions. The geometry is given by Verdon
[1987a] and is repeated here for convenience. The cascade has a stagger
angle, g, of 45o and a gap/chord ratio, t, of unity. The blades are constructed
by superimposing the thickness distribution of a modified NACA four digit
series airfoil on a circular arc camber line. The thickness distribution
is given by: (3.10.1) where HT is the nominal blade thickness. The coefficient
of the x4 in eq. (3.10.1) differs from that used in the standard NACA airfoil
definition (i.e., - 1.015) so that the example blades will close in as
wedge-shaped trailing edges. The camber distribution is given by: (3.10.2)
where HC (>0) is the height of the camber-line at midchord and is the
radius of the circular arc camber line. The surface coordinates of the
reference blade are therefore given by: (3.10.3) where the signs + and
- refer to the upper (suction) and lower (pressure) surfaces, respectively,
and q=tan-1(dC/dx). For the present example we set HT=0.06 and HC=0.05
to study the unsteady aerodynamic response of a vibrating cascade of cambered
NACA 0006 airfoils. We consider two different steady-state inlet operating
conditions. In the aeroelastic cases 1-16 the inlet Mach number, M1, and
flow angle, b1, are 0.7 and - 55o, respectively; for cases 17-32, M1=0.8
and b1=- 58o (see Table 3.10.1). The flow through the cascade is assumed
to satisfy a Kutta condition at blade trailing edges and, therefore, only
inlet flow information must be specified. For M1=0.7 and b1=-55o, the mean
or steady flow through the cascade is entirely subsonic; for M1=0.8 and
b1=-58o it is transonic with a normal shock occurring in each blade passage.
As aeroelastic test cases we consider single-degree- of-freedom blade heaving,
normal to chord, and pitching motions at four different frequencies, k=0.25,
0.50, 0.75 and 1.0, and at interblade phase angles lying in the range -p_s_p.
The amplitude of the heaving motion, h, is 0.01; that of the pitching motion,
a, is 2o. The blade pitching axis lies at midchord, i.e. (xa,ya)=(0.5,0.05).
We are interested in the following aerodynamic response information for
each of the two inlet operating conditions given, at reduced frequencies
of k=0.25, 0.50, 0.75 and 1.0 (see Table 3.10.1 for details): 1: The time-averaged
blade surface pressure coefficient, and Mach number. 2: a: Amplitude, ,
and phase lead angle, , of the unsteady blade surface pressure coefficient
for heaving and pitching motions at s=0o and s=90o. b: Amplitude, , and
phase lead angle, , of the unsteady blade surface pressure difference coefficient
for heaving and pitching motions at s=0o and s=90o. 3: a: The amplitude,
, and phase lead angle, , of the unsteady lift coefficient per unit amplitude
vs interblade phase angle for the heaving motions at -p_s_p. b: The amplitude,
, and phase lead angle, , of the unsteady moment coefficient per unit amplitude
vs interblade phase angle for the pitching motions at -p_s_p. 4: The aeroelastic
damping coefficient, X, vs interblade phase angle for the heaving and pitching
motions at -p_s_p. Usab and Verdon [1990, 1989b, 1987a,c], and Whitehead
[1990] have already presented results on this cascade. Results from other
prediction models were also recently presented [Huff, 1991; Hall, 1991].
Some very promising results have been obtained (these will be included
in the complete updated report presently in preparation). When comparing
these results with each other it must be considered that no analytical
results exist. Only the mutual agreement between several similar theoretical
methods can thus indicate the accuracy of the models. Stagger angle: g
=45o Gap/chord: t =1.0 Pitch axis: (xa,ya) = (0.5,0.05)